疾病流行过程的混沌分析方法

Chaotic Analysis Method in Epidemic

目的介绍混沌分析方法在研究疾病流行过程中的应用，并对辽宁省本溪市１９５５～１９９６年的百日咳逐月发病数进行分析。方法利用混沌动力学相空间重构技术，给出某种疾病月发病数Ｘｔ的时间趋势图、混沌相图和递次振幅图，通过递次振幅图的分布特点及谱分析，确定某种疾病流行的动力系统是否混沌，对呈混沌流行的疾病求其关联分维，判定其混沌程度。结果辽宁省本溪市１９５５～１９９６年的百日咳流行是混沌的，动力性态符合一个受噪声摄动的高－低４年循环，逐月发病数Ｘｔ具有混沌分布的迭代模型。本溪百日咳流行过程奇怪吸引子的分维值为２．６６７，其中计划免疫前分维值为２．７２２，计划免疫后分维值降为１．９３８，说明百日咳流行过程中相空间轨迹存在有规则周期性或向平稳状态发展的趋势。

Object To introduce the chaotic analysis method in epidemic,and to analyze the monthly reported cases of pertussis in Benxi city in the periods 1955 1996.Methods The reconstruction technique of phase space,the time series,Poincare section,power spectra and correlation fractal dimension were used.Results The dynamic system of Benxi pertussis was chaotic,the correlation dimension was 2 667,before vaccination the dimension was 2 722,after vaccination changed to 1 938.And the cycle of pertussis outbreaks approximate 4 years.Conclusion With these methods,those non stochastic dynamic systems in epidemic would be studied correctly.